Finite Group Databasebeta

← C22×C42×C3⋊D3 #11899790

Subgroups — C22×C42×C3⋊D3 #11899790

Order 1152.

9000 conjugacy classes of subgroups; only the 2745 normal subgroups are shown.

normal subgroups only

This group has 9000 conjugacy classes of subgroups — too many to draw. Only its 2745 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C213yesmaximal
2C22×C32×C42C211yesmaximal, characteristic, complemented
3C22×C4×C3⋊Dic3C213yesmaximal, complemented
4C2×C42×C3⋊D3C2124yesmaximal, direct product factor
5C22×C42×D3—34nomaximal
6C24×C3⋊D3C2211yescharacteristic
7C23×C32×C4C2213yes—
8C23×C3⋊Dic3C2213yes—
9C22×C4×C3⋊D3C4148yesdirect product factor
10C22×C4×C3⋊D3C22136yes—
11C2×C32×C42C22112yescomplemented
12C2×C4×C3⋊Dic3C22136yescomplemented
13C42×C3⋊D3C22164yesdirect product factor
14C23×C4×D3—312no—
15C22×C3×C42D314yescomplemented
16C22×C4×Dic3—312no—
17C2×C42×D3—396no—
18C24×C32C2311yescharacteristic
19C23×C3⋊D3C2×C4124yes—
20C23×C3⋊D3C2316yes—
21C22×C32×C4C2×C4124yescomplemented
22C22×C32×C4C23118yes—
23C22×C3⋊Dic3C2×C4124yescomplemented
24C22×C3⋊Dic3C23118yes—
25C2×C4×C3⋊D3C2×C41288yesdirect product factor
26C2×C4×C3⋊D3C23148yes—
27C32×C42C23116yescomplemented
28C4×C3⋊Dic3C23148yescomplemented
29C23×C42—91noSylow
30C24×D3—34no—
31C23×C3×C4C2×D3112yes—
32C23×Dic3—312no—
33C22×C4×D3—3192no—
34C22×C4×D3—3144no—
35C2×C3×C42C2×D3148yescomplemented
36C2×C4×Dic3—3144no—
37C42×D3—3256no—
38C23×C32C22×C4112yes—
39C23×C32C2413yes—
40C22×C3⋊D3C42164yesdirect product factor
41C22×C3⋊D3C22×C4172yes—
42C22×C3⋊D3C2414yes—
43C2×C32×C4C22×C4172yescomplemented
44C2×C32×C4C24112yes—
45C2×C3⋊Dic3C22×C4172yescomplemented
46C2×C3⋊Dic3C24112yes—
47C4×C3⋊D3C22×C41192yesdirect product factor
48C24×C4—93no—
49C22×C42—93no—
50C22×C42—924no—
51C22×C42C3⋊D311yescharacteristic, direct product factor
52C24×C3C22×D314yes—
53C23×D3—396no—
54C23×D3—324no—
55C22×C3×C4C4×D3196yescomplemented
56C22×C3×C4C22×D3172yes—
57C22×Dic3—396no—
58C22×Dic3—372no—
59C2×C4×D3—31152no—
60C2×C4×D3—3192no—
61C3×C42C22×D3164yescomplemented
62C4×Dic3—3192no—
63C22×C32C2×C42116yescomplemented
64C22×C32C23×C4118yes—
65C22×C32C2511yescharacteristic
66C2×C3⋊D3C2×C42196yesdirect product factor
67C2×C3⋊D3C23×C4124yes—
68C32×C4C23×C4124yescomplemented
69C3⋊Dic3C23×C4124yescomplemented
70C25—91no—
71C23×C4—93no—
72C23×C4—948no—
73C23×C4—936no—
74C23×C4C2×C3⋊D313yes—
75C2×C42—936no—
76C2×C42—964no—
77C2×C42C2×C3⋊D3112yesdirect product factor
78C23×C3C2×C4×D3148yes—
79C23×C3C23×D3112yes—
80C22×D3—3256no—
81C22×D3—3288no—
82C22×D3—316no—
83C2×C3×C4C2×C4×D31288yescomplemented
84C2×C3×C4C23×D3148yes—
85C2×Dic3—3288no—
86C2×Dic3—348no—
87C4×D3—3768no—
88C2×C32C22×C42112yescomplemented
89C2×C32C24×C413yes—
90C3⋊D3C22×C42116yesdirect product factor
91C24—96no—
92C24—924no—
93C24C22×C3⋊D311yescharacteristic
94C22×C4—918no—
95C22×C4—924no—
96C22×C4—948no—
97C22×C4—9288no—
98C22×C4C4×C3⋊D3124yesdirect product factor
99C22×C4C22×C3⋊D3118yes—
100C42—948no—
101C42C22×C3⋊D3116yesdirect product factor
102C22×C3C42×D3164yescomplemented
103C22×C3C22×C4×D3172yes—
104C22×C3C24×D314yes—
105C2×D3—396no—
106C2×D3—3384no—
107C3×C4C22×C4×D3196yescomplemented
108Dic3—396no—
109C32C23×C4211yescharacteristic, complemented, Sylow
110C23—964no—
111C23—972no—
112C23—94no—
113C23C2×C4×C3⋊D3112yes—
114C23C23×C3⋊D313yes—
115C2×C4—972no—
116C2×C4—912no—
117C2×C4—9192no—
118C2×C4C2×C4×C3⋊D3172yesdirect product factor
119C2×C4C23×C3⋊D3112yes—
120C2×C3C2×C42×D3148yescomplemented
121C2×C3C23×C4×D3112yes—
122D3—364no—
123C22—996no—
124C22—924no—
125C22C42×C3⋊D3116yesdirect product factor
126C22C22×C4×C3⋊D3118yes—
127C22C24×C3⋊D311yescharacteristic
128C4—924no—
129C4C22×C4×C3⋊D3124yesdirect product factor
130C3C22×C42×D314yescomplemented
131C2—916no—
132C2C2×C42×C3⋊D3112yesdirect product factor
133C2C23×C4×C3⋊D313yes—
subgroupG/H
center, hypercenterC22×C42C3⋊D3
commutator, hypocenterC32C23×C42
FrattiniC22C24×C3⋊D3
FittingC22×C32×C42C2
socleC24×C32C23
prime radicalC24×C3⋊D3C22
cosocleC22×C32C25
LCSG ▷ C32
UCSC1 ◁ C22×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C32×C42C2semidirect
3. C22×C4×C3⋊Dic3C2semidirect
4. C2×C42×C3⋊D3C2direct (N × H)
9. C22×C4×C3⋊D3C4direct (N × H)
11. C2×C32×C42C22semidirect
12. C2×C4×C3⋊Dic3C22semidirect
13. C42×C3⋊D3C22direct (N × H)
15. C22×C3×C42D3semidirect
21. C22×C32×C4C2×C4semidirect
23. C22×C3⋊Dic3C2×C4semidirect
25. C2×C4×C3⋊D3C2×C4direct (N × H)
27. C32×C42C23semidirect
28. C4×C3⋊Dic3C23semidirect
35. C2×C3×C42C2×D3semidirect
40. C22×C3⋊D3C42direct (N × H)
43. C2×C32×C4C22×C4semidirect
45. C2×C3⋊Dic3C22×C4semidirect
47. C4×C3⋊D3C22×C4direct (N × H)
51. C22×C42C3⋊D3direct (N × H)
55. C22×C3×C4C4×D3semidirect
61. C3×C42C22×D3semidirect
63. C22×C32C2×C42semidirect
66. C2×C3⋊D3C2×C42direct (N × H)
68. C32×C4C23×C4semidirect
69. C3⋊Dic3C23×C4semidirect
77. C2×C42C2×C3⋊D3direct (N × H)
83. C2×C3×C4C2×C4×D3semidirect
88. C2×C32C22×C42semidirect
90. C3⋊D3C22×C42direct (N × H)
98. C22×C4C4×C3⋊D3direct (N × H)
101. C42C22×C3⋊D3direct (N × H)
102. C22×C3C42×D3semidirect
107. C3×C4C22×C4×D3semidirect
109. C32C23×C42semidirect
118. C2×C4C2×C4×C3⋊D3direct (N × H)
120. C2×C3C2×C42×D3semidirect
125. C22C42×C3⋊D3direct (N × H)
129. C4C22×C4×C3⋊D3direct (N × H)
130. C3C22×C42×D3semidirect
132. C2C2×C42×C3⋊D3direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C4×C3⋊D32
C22×C32×C422
C22×C4×C3⋊Dic32
C2×C42×C3⋊D32
C22×C42×D33